Question

A guidance counselor at a local high school is interested in determining what, if any, linear relationship there is between high school percentile ranks and college GPAS. A student's percentile rank is calculated by determining the percentage of all students in the graduating class with a final high school GPA at or below his or hers. For example, a student graduating 10th in a class of 300 would have a percentile rank (to one decimal place) of (290/300)x100 - 96.7. SUMMARY OUTPUT Regression Statishes Multiple R 0.42853296 R Square 0.183540498 Adjusted R Square 0.163443071 0.595165667 Observations 4137 ANOVA dr SS MS F S 1 329 487 329 487 930. 1704 4135 1464 709 0 354222 4136 1794 196 on ficance F 1.8886E-184 Regression Residual Total Coefficienta tandard Em Staf P value Lower 95% Upper 95% Intercept 1 276875668 0046049 27.72907 23E-155 1.186615795 1367177542 Percentile Rank 0 011034905 0.000559 30 4987 19.184 0.015939056 0.018129954 Interpret the value of R2 in the context of the problem About 3.2% of college GPAs will be able to be perfectly estimated using the variability in the fitted regression line About 82% of the variability in college GPAs can be explained," or accounted for, by the regression fit between college GPA and high school percent rank About 57% of the variability in college GPAs can be explained, or accounted for by the regression it between college GPA and high school percentile rank. About 43 of the variability in college GPAs can be explained." or accounted for by the regression fit between college GPA and high school percent le rank

Answer 1

Here, we have to fit the linear regression model between high school percentile rank and college GPAs.

Since, value of Multiple R is 0.42853296

Thus, interpretation of R2 is given by,

(d) About 43% of the variability in college GPAs can be"explained" or accounted for, by the regression fit between college GPAs and high school percentile rank.